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From: hallyb@globbo.enet.dec.com (John Hallyburton)
Newsgroups: comp.ai.neural-nets
Subject: NN solution of non-deterministic problems.  Doable or stupid?
Message-ID: <14121@shlump.nac.dec.com>
Date: 1 Aug 90 00:40:39 GMT
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Organization: Twin Peaks Municipal Software Works
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There's a lot of brainpower in this newsgroup; please forgive me if
this turns out to be a stupid question.  I don't mean to lower the
average level of discussion!

I'd like to know if it's possible to use neural nets to solve problems
that aren't fully deterministic, that is, similar inputs produce two or
more different outputs in different training cases.

One simple example is in the field of weather forecasting.  Suppose we
want to forecast next week's Duluth rainfall.  We might input various
training cases over the last 40 years, including such data as the local
rainfall last week, two weeks ago, ..., last Winter's snowfall in the
Rockies, the temperature of the Pacific Ocean at various stations, the
phase of the moon, etc., the list goes on and on.

When you boil it down to basics, so to speak, you will end up with
training cases that have repeated inputs and different outputs.  What
could I expect a good neural net program to produce?  Taking a simple
example where A, B, and C are constants and there is only one output
(rainfall total in inches), history might give us the following cases:

	A, B, C,    0
	A, B, C,    5
	A, B, C,    5
	A, B, C,    6

Would most neural nets decide the correct output for (A, B, C) is the
average, 4?

Would there be any way to construct extra outputs that serve as sort of
a confidence indicator, so that the reader could see not only a forecast
"4 inches of rain expected next week", but also get a feeling for its
accuracy, optimally yielding a forecast like "75% chance of rain with
about 5 inches expected.  Get that corn planted".

If the number of inputs is small one could code up a solution using more
traditional programming techniques.  But if there are 100 inputs then it
becomes impractical to try to look at every possible subset of the inputs
to determine what was obviously 75% in the example above.

Any thoughts appreciated.

  John (usual disclaimers)